
Anyone can file a DMCA notice. The recipient of the notice can decide in its sole discretion whether to abide by the notice. In general, only compliance with the takedown demand provides the recipient of the notice with the "safe harbor" provided by the DMCA. In general, the recipient of the notice does not get involved in trying to decide copyright-law issues such as fair use.
Other Answers
When a collaborative work is prepared, the copyright in the collaborative work does not extend to the copyrights in the individual works that make up the overall work. It is possible that the copying, public display, etc. of a collaborative work infringes the copyright of one or more of the copyrights of the individual works in the collaborative work. The answer to your question will probably depend on the agreement that the project has with the owner of the copyright in the individual work. If the agreement gives a license to the individual work in the collaborative work, then the DMCA claim shouldn't stand because the project has authorization to the individual work. This license could be written, or it could be oral. There may be a fair use here, there really aren't enough facts to tell. Fair use depends on a lot of factors, the non-commercial aspect being only one of them. You should consult an attorney knowledgeable of copyright law to answer your questions.